Exploding solitons and Shil'nikov's theorem

Nail Akhmediev*, J. M. Soto-Crespo

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    52 Citations (Scopus)

    Abstract

    We have performed a detailed linear stability analysis of exploding solitons of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We have found, numerically, the whole set of perturbation eigenvalues for these solitons. We propose a scenario of soliton evolution based on this spectrum of eigenvalues. We relate exploding and self-restoring behavior of solitons to the Shil'nikov theorem, and point out common features and differences between our system, with an infinite number of degrees of freedom, and Shil'nikov's system with three degrees of freedom.

    Original languageEnglish
    Pages (from-to)287-292
    Number of pages6
    JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
    Volume317
    Issue number3-4
    DOIs
    Publication statusPublished - 20 Oct 2003

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